Influence of Pore Size on the van der Waals Interaction in Two-Dimensional Molecules and Materials

Despite the importance of porous two-dimensional (2D) molecules and materials in advanced technological applications, the question of how the void space in these systems affects the van der Waals (vdW) scaling landscape has been largely unanswered. Analytical and numerical models presented herein demonstrate that the mere presence of a pore leads to markedly different vdW scaling across nonasymptotic distances, with certain relative pore sizes yielding effective power laws ranging from simple monotonic decay to the formation of minima, extended plateaus, and even maxima. These models are in remarkable agreement with first-principles approaches for the 2D building blocks of covalent organic frameworks (COFs), and reveal that COF macrocycle dimers and periodic bilayers exhibit unique vdW scaling behavior that is quite distinct from their nonporous analogs. These findings extend across a range of distances relevant to the nanoscale, and represent a hitherto unexplored avenue towards governing the self-assembly of complex nanostructures from porous 2D molecules and materials.